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Why random portfolios appear to outperform benchmarks...
11 responses

This is certainly interesting based off of scanning the first page. I remember that I use to try to implement a momentum strategy and found it to be delivering negative premia over time. So the logical thinking would be to invert it (into a mean-revert strategy) and have it deliver AMAZING alpha. obviously that was not the case. Reading this article will definitely allow me to understand more of this phenomenon

I just read the article I'm still not sure how a strategy and it's inverse can have negative returns, can you please elaborate?

Ari, the authors argue that through the Fama-French decomposition, they found that even if you invert each strategy, the outperformance is the result of having more exposure to value based portfolios.

So they talk about a long-only strategy, and its 'inverse', which is also long only. (That wouldn't be my intuitive understanding of an inverse strategy from a time-series point of view - I'd expect it go short where it went long - but from a weighting point of view it does make sense). They use either 1/w (and normalise) or max(w)-w (and normalise).

I assume when they are talking about price they are literally referring to the stock price?

@James.. Inverse strategy ' inverse' ETF... how does it woks...? and how come.. there is no sample algo in quantopian using inverse strategy... they seem.. to outperform the benchmark.

I believe that you surmise correctly regarding the weighting vs. inverse weighting (long only) as opposed to inverse positions (long and short). However, raw price alone is not used as a criteria for weighting. There are numerous criteria used for weighting as shown in Exhibit 1. They use that table to show that capitalization weighting (as in market indices) is a poor choice which under-performs NUMEROUS other portfolio weighting criteria.

Exhibit 1 is very interesting, I hadn't fully appreciated it. For the "High Risk = High Reward" strategies, the one which stands out to me is the "Inverse-Ratio of Market Beta Weighted" strategy which manages to have higher returns and lower standard deviation than the original strategy. I suppose some middle-ground between that and the "Minimum Variance" strategy would be ideal.

But what I mean is, in Appendix A, the last 4 paragraphs refer to price: "By design, a cap-weighted portfolio has larger allocations to the higher-price stocks, which have lower returns."
If that were the case, I could just select low-priced stocks, no? Am I missing something?

Perhaps there should be.

If that were the case, I could just select low-priced stocks, no? Am I missing somethin

Indeed. You are referring to the small-cap anomaly.

Exhibit 1 does have a nice shopping list of algos for experimentation.

The author appears to be using the term "price" loosely. I believe that he always means price in relationship to something else throughout the article. He seems to be using the term "price" as a proxy for capitalization in Appendix A as indicated in parenthesis since price x shares = capitalization. However, it seems obvious that price alone would not a good proxy for capitalization due to differences in the number of shares outstanding. After all, when a stock splits 2:1, the company's capitalization remains the same even though its shares are now half the price.

Thank you that has made good reading.

Hmm, perhaps he just means 'on average'? Stocks tend to split in order to keep in a sensible price range...